To register a DBA to be owned by a business entity, such as an LLC, the parent company would have to be registered in the state the DBA would be registered in, respectively.
That being said, you would really have two options to consider:
The first option is that you could form a new business entity in California, and then register a DBA underneath it (or just use the name you want for DBA as a company name). This means you would have two separate businesses, with two separate EIN numbers, and subsequently documents such as Operating Agreements or company bank accounts.
The second option is that you can file your New Mexico LLC as a foreign entity in California, having your original business name and EIN registered in both states as active entities, where you could then register a DBA in California.